Which conic is x^2 - 8y = 0

Step by step, with the reason for every step · Conics from the general form · Precalculus

Step by step

Question: name the conic and write in standard form x² − 8y = 0.

x² − 8y = 0

Look at the squares.

Only x² is here.

So it is a parabola.

only x² or only y² → parabola ✓

x² and y², same number in front → circle

same signs, different numbers → ellipse

different signs → hyperbola

Keep the x terms on the left.

Move − 8y and the plain number to the right: their signs change.

(x²) = 8y

That is the standard form of a parabola: x² = 8y.

Let's check with a point on it, (4, 2).

Put it in the first equation.

4² − 8 × 2 = 16 − 16 = 0

We get 0, like the first equation says.

So the standard form is right!

Let's look back.

First: name the conic.

Then: keep x on the left.

Last: check.

Answer

(x²) = 8y

Try this one yourself, then check:

Name the conic and write in standard form x² − 4y = 0

Show the answer

x² = 4y